Asked by sarah
Given the function f(x) = 2(3)^x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.
Part A: Find the average rate of change of each section.
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other.
Part A: Find the average rate of change of each section.
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other.
Answers
Answered by
Steve
f(x) = 2*3^x
on [0,1] the average rate is
(f(1)-f(0)))/(1-0) = (2*3^1 - 2*3^0)/1 = 6-2 = 4
on [2,3] the average rate is (f(3)-f(2))/(3-2) = (2*3^3 - 2*3^2)/1 = 54-18 = 36
the ratio of the rates is 36/4 = 9.
The reason the rate increases is that exponentials grow ever faster. The larger x gets, the steeper the curve is. The rate of change is proportional to the function value.
on [0,1] the average rate is
(f(1)-f(0)))/(1-0) = (2*3^1 - 2*3^0)/1 = 6-2 = 4
on [2,3] the average rate is (f(3)-f(2))/(3-2) = (2*3^3 - 2*3^2)/1 = 54-18 = 36
the ratio of the rates is 36/4 = 9.
The reason the rate increases is that exponentials grow ever faster. The larger x gets, the steeper the curve is. The rate of change is proportional to the function value.
Answered by
sarah
Thank you so much Steve :)
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